The beta distribution as a probability model for daily cloud duration

This paper reports on the adequacy of the beta distribution as a model for frequency distribution of daily cloud duration. Daily cloud duration is defined here as the fraction of observable daylight hours not receiving bright sunshine. Data from 11 Australian locations, representing a variety of climatic types, were used to construct 132 (11 stations by 12 months) empirical frequency distributions of daily cloud duration. Statistical tests showed that the beta distribution fitted well and significantly better than the logit normal distribution. The beta distribution is a simple and flexible two-parameter distribution that can be fitted given only the sample mean and variance of daily cloud duration. Furthermore, it is shown that the variance of cloud duration may be reasonably estimated from the mean cloud duration using a simple empirical relationship. This is of practical importance as the mean daily cloud duration is widely tabulated for many locations around the world, making it possible to estimate the empirical cloud duration frequency for sites without readily accessible daily recorded data.